Google search results for my site have strange titles and missing descriptions.

Google DOES NOT have to use your title tags nor does it have to use your meta descriptions. They use whatever their algorithm thinks will generate more clicks for any given query. Depending what someone searches for, they may use your titles and meta descriptions sometimes and for other queries, they may not.

I'm not sure anyone definitively knows when or how Google makes that determination but it is my belief that they split test which is better for clicks - what you wrote or the text that they grabbed from your page - and whatever gets the most clicks for any given search query is what they use.

I'm quite sure that if what you wrote as your title tag and meta description has little to do with what is actually on your page, they will not use either.

Hi , I thing you shout not proper SEO Plugin , and not proper submit title tags and meta description according according to SEO norms , title tag and meta description tenth according to Google , I thing you use SEO Premium Plugin on website and proper submit on google webmaster for Crowling and indexing ,
Thanks
Narmadatech

Hi heera, what is name of your website. And i guess the mistake was with the Plugin you installed. Uninstall and go for Yoast SEO plugin or all in one SEO plugin.

Pretty sure its a mistake made by you or the SEO plugin you are using or if you are using a nulled theme/plugin then its pretty normal since your website could be hacked.

Check them properly and you will be fix that issue.